Question: Solve for $x$ and $y$ using elimination. ${-2x+3y = 19}$ ${-5x-5y = -65}$
Solution: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $5$ and the bottom equation by $3$ ${-10x+15y = 95}$ $-15x-15y = -195$ Add the top and bottom equations together. $-25x = -100$ $\dfrac{-25x}{{-25}} = \dfrac{-100}{{-25}}$ ${x = 4}$ Now that you know ${x = 4}$ , plug it back into $\thinspace {-2x+3y = 19}\thinspace$ to find $y$ ${-2}{(4)}{ + 3y = 19}$ $-8+3y = 19$ $-8{+8} + 3y = 19{+8}$ $3y = 27$ $\dfrac{3y}{{3}} = \dfrac{27}{{3}}$ ${y = 9}$ You can also plug ${x = 4}$ into $\thinspace {-5x-5y = -65}\thinspace$ and get the same answer for $y$ : ${-5}{(4)}{ - 5y = -65}$ ${y = 9}$